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Let's break down the problem:

We are given the following information:
- A packet of grass seed covers **50 m²** of lawn.
- The lawn is circular with a **diameter of 20 meters**.

### Step 1: Calculate the area of the circular lawn
The formula for the area $ A $ of a circle is:
\[
A = \pi r^2
\]
where $ r $ is the radius of the circle. The radius is half the diameter, so:
\[
r = \frac{20}{2} = 10 \, \text{meters}
\]
Now, using the formula for the area:
\[
A = \pi \times (10)^2 = 100 \pi \, \text{square meters}
\]
\[
A \approx 100 \times 3.1416 = 314.16 \, \text{m²}
\]

### Step 2: Determine the number of seed packets needed
Since one packet covers **50 m²**, the number of packets required is:
\[
\text{Packets needed} = \frac{\text{Total area of lawn}}{\text{Area covered by one packet}} = \frac{314.16}{50} \approx 6.28
\]
Since you can't buy a fraction of a packet, you will need to round up to the nearest whole number, so you need **7 packets**.

Would you like more details or have any questions?

Here are 5 related questions for further exploration:
1. What would be the number of packets if the diameter was doubled?
2. How many square meters can 3 packets of grass seed cover?
3. What is the cost if each packet of seed costs $5?
4. How does the area change if the radius is increased by 5 meters?
5. What would be the area if the lawn were an ellipse instead of a circle?

**Tip**: When solving problems involving areas of circles, remember that the area grows with the square of the radius, so small increases in radius lead to much larger areas.

A packet of grass seed can be used to cover 50m² of lawn. A circular lawn has a diameter of 20 metres. How many packets of grass seed must be bought so that the entire lawn can be covered?

Find out how many packets of grass seed are needed to cover a circular lawn with a diameter of 20 meters. This step-by-step solution involves calculating the area of the lawn using the formula for the area of a circle and determining the number of packets required. Perfect for students in Grades 6-8.

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